|
|
A005489
|
|
Number of nonzero coefficients of order n in Baker-Campbell-Hausdorff expansion.
(Formerly M0181)
|
|
1
|
|
|
1, 1, 2, 1, 8, 7, 32, 31, 96, 97, 512, 511, 2048, 2047, 7396, 7531, 32768, 32767, 131072, 131071, 508436, 512245, 2097152, 2097151, 8202208, 8207797, 33256980, 33335611, 134217728, 134217727, 536870912, 536870911, 2142108916, 2143603741, 8589928768, 8589921949
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
LINKS
|
|
|
MATHEMATICA
|
g[1] = 1;
g[s_] := g[s] = Expand[(2 t - 1) g[s - 1] + t (t - 1) D[g[s - 1], t]];
cx[ss_] := Module[{m, mp, mpp, \[Gamma]},
m = Length[ss] + 1;
mp = Floor[m/2];
mpp = Floor[(m - 1)/2];
\[Gamma] = CoefficientList[Product[g[s], {s, ss}], t];
(-1)^mpp mpp! / Product[s!, {s, ss}] Sum[\[Gamma][[k]] (mp + k - 1)!/(m + k - 1)!, {k, Total[ss] - m + 2}]
];
cxs[n_] := Select[Table[{cx[ss], Length@Permutations@ss}, {ss, IntegerPartitions[n - 1]}], First@# != 0 &];
a[n_] := Total[Last /@ cxs[n]];
Table[a[n], {n, 10}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
David J. Thompson
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|